Non-self-similar, linear dynamics during pinch-off of a hollow annular jet

Based on an experimental and computational study of the breakup of a drop (jet) of small viscosity in an ambient fluid of large viscosity, Doshi et al. [Science 302, 1185 (2003)] have shown that the breakup of a drop (jet) of zero viscosity in a very viscous ambient fluid gives rise to an unexpected, nonuniversal form of singularity. Doshi et al. conjectured that the nonuniversal dynamics result from the fact that stresses exerted by the inner fluid are negligible. To verify this conjecture and overcome computational difficulties associated with simulating systems in which the disparity between the viscosities of the inner and the outer fluids is large, the breakup of an annular jet whose core is a gas of negligible viscosity is analyzed. Calculations show that as the jet’s minimum radius hmin→0, both core- and shell-side pressures remain bounded while surface tension pressure, which diverges as 1/hmin, is balanced by viscous normal stress exerted by the shell fluid. Simulations show that interfacial points move radially inward with the same velocity. Fourier decomposition of interface shapes confirms that the dynamics are linear. As hmin→0, the axial length scale remains finite, its value varying with imposed initial and boundary conditions. Thus, the breakup is not self-similar and the final breakup profile is nonuniversal.